WASHINGTON STATE MATHEMATICS COUNCIL 1999 MIDDLE SCHOOL MATH OLYMPIAD SEVENTH GRADE PROBABILITY & STATISTICS Make sure you include proper units in your answer! 7

1. Ted has 30 bills of different dollar values stuffed in a jar in his room. There are twice as many ones as there are fives. There are four times as many ones as there are tens. There are twice as many tens as there are twenties. If Ted reaches into the jar and randomly pulls out a bill, what is the probability that the bill will be a twenty? [State the probability in fraction form.]

2. The Mount Kamiah seventh grade class is about to hold elections. There are four elected positions: President, Vice President, Secretary, and Treasurer. There are only 28 students in the Mount Kamiah seventh grade class, and they are all eligible to hold any one of the four offices. How many possible outcomes of the election are possible with this class of 28 students if no student can hold more than one office?

3. Twelve students have volunteered to provide data for a study. The following data have already been collected:

 Amy Bill Ché Don Eva Fred Gina Hope Ian Julie Kim Lara 11 19 25 10 11 20 6 8 17 23

The data for Kim and Lara are identical. The median of the data is equal to the mean of the data, and both of these are equal to the data for Kim and Lara. What is this number?

 4 The students in Ms. Hopkins' algebra class collected data from the students in their school that resulted in the percentages at right. What is the fewest number of students who could have contributed data to the study? Favorite Pet Cat 25% Dog 24% Horse 20% Bird 16% Hamster 12.5% Lizard 2.5%

5. If the squares of the first 20 positive numbers are used as a sample, what four digits (0 through 9) have the highest probability of being found in the one's place of the squares of positive numbers?